The repeating decimal, 0.27 ..., is converted to the fraction 0.27 ... = 3/x

what is the value for x in the fraction

311

Explanation:

You can do this with a bit of algebra, let x=0.27272727 ...

Now times by 100 to get 100x=27.27272727 ...

But we can get rid of that tail part now by taking off x=0.272727 ..., so

100x-x=99x=27

Now just divide by 99 to get that x = 2799 = 311